The Vector Function for Distance Travelled in Great Circle Navigation

摘要

Traditionally, on a great circle, the latitude or longitude of a waypoint is found by inspection. In this paper, using an elementary knowledge of vector algebra including linear combination of vectors and vector basis, we provide an easy method for finding the equation of a great circle path as a parameterized curve. By use of this vector function of distance travelled, the latitude and longitude of waypoints can be found based on the distance from departure point along a great circle. The approach is intended to appeal to the navigator who is interested in the mathematics of navigation and who, nowadays, solves his navigation problems with a personal computer.